Branching Pomsets for Choreographies

Abstract

Choreographic languages describe possible sequences of interactions among a set of agents. Typical models are based on languages or automata over sending and receiving actions. Pomsets provide a more compact alternative by using a partial order over these actions and by not making explicit the possible interleaving of concurrent actions. However, pomsets offer no compact representation of choices. For example, if an agent Alice can send one of two possible messages to Bob three times, one would need a set of 2 × 2 × 2 distinct pomsets to represent all possible branches of Alice's behaviour. This paper proposes an extension of pomsets, named branching pomsets, with a branching structure that can represent Alice's behaviour using 2 + 2 + 2 ordered actions. We encode choreographies as branching pomsets and show that the pomset semantics of the encoded choreographies are bisimilar to their operational semantics.

Realisability of Branching Pomsets

“…Infinity The paper introducing branching pomsets [13] supports branching pomsets of infinite size. We note that our theoretical results in this paper also hold for infinite branching pomsets.…”

“…In this section we recall the concept and definitions of branching pomsets. This section is heavily based on the original introduction of branching pomsets [13]; a more thorough explanation can be found in that paper.…”

“…Finally, the fourth rule overloads the refinement notation to also apply to branching pomsets themselves: if R.B can refine to some B , then R itself can refine to a derived branching pomset with branching structure B , whose events are restricted to those occurring in B and likewise for ≤ and λ -as defined in Figure 2c. We note that we omit one of the rules in [13], since our later well-formedness conditions lead to it never being used.…”

“…Multiple choices result in one pomset for each possible combination of branches, which can yield an exponentially large set of pomsets. Recent work by the authors and Proença and Cledou introduces branching pomsets [13]. These extend pomsets with a branching structure to compactly represent both concurrency and choices, avoiding both exponential blowups.…”